Upscaling of a two-region façade-leaching model to the city scale

Painted facades are protected by paints that contain biocides as a protection against degradation. These facades are leached of biocides by rainfall, albeit at low concentrations. Nevertheless, at the city scale the leachable surface area of building facades is significant, and thus there is potential for biocides to enter receiving waters. A city-scale estimation method was developed based on two main steps. In the first step, a series of laboratory experiments on a single facade was used to calibrate and validate a 1D, two-region phenomenological model of biocide leaching. The same data set was analyzed independently by another research group who found empirically that biocide leachate breakthrough curves were well represented by a sum of two exponentials. Interestingly, the two-region model was found analytically to reproduce this functional form as a special case. The second step in the method was to upscale the single facade model. Here, GIS-based estimates of facade length and area were deduced using cadastral data. Paint application rates were modeled as a stochastic process based on manufacturers’ recommendations. The methodology was applied in an example application for Lausanne, Switzerland, a city of about 200,000 inhabitants. The ratio of biocide transferred from facades to the environment was estimated at about 30% of annual mass applied.